An additivity formula for the strict global dimension of C(Ω)

Seytek Tabaldyev

Open Mathematics (2014)

  • Volume: 12, Issue: 3, page 470-475
  • ISSN: 2391-5455

Abstract

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Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .

How to cite

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Seytek Tabaldyev. "An additivity formula for the strict global dimension of C(Ω)." Open Mathematics 12.3 (2014): 470-475. <http://eudml.org/doc/269153>.

@article{SeytekTabaldyev2014,
abstract = {Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .},
author = {Seytek Tabaldyev},
journal = {Open Mathematics},
keywords = {Strict Banach algebra; Strict projective module; Strict global homological dimension; strict Banach algebra; strict projective module; strict global homological dimension},
language = {eng},
number = {3},
pages = {470-475},
title = {An additivity formula for the strict global dimension of C(Ω)},
url = {http://eudml.org/doc/269153},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Seytek Tabaldyev
TI - An additivity formula for the strict global dimension of C(Ω)
JO - Open Mathematics
PY - 2014
VL - 12
IS - 3
SP - 470
EP - 475
AB - Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .
LA - eng
KW - Strict Banach algebra; Strict projective module; Strict global homological dimension; strict Banach algebra; strict projective module; strict global homological dimension
UR - http://eudml.org/doc/269153
ER -

References

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  3. [3] Khelemskiĭ; A.Ya., Smallest values assumed by the global homological dimension of Banach function algebras, Amer. Math. Soc. Transl., 1984, 124, 75–96 
  4. [4] Krichevets A.N., On homological dimension of C(Ω), VINITI preprint #9012-B86, 1986 (in Russian) 
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  9. [9] Selivanov Yu.V., The values assumed by the global dimension in certain classes of Banach algebras, Moscow Univ. Math. Bull., 1975, 30(1), 30–34 Zbl0307.46037
  10. [10] Selivanov Yu.V., Homological dimensions of tensor products of Banach algebras, In: Banach Algebras’ 97, Blaubeuren, July 20–August 3, 1997, Walter de Gruyter, Berlin, 1998, 441–459 Zbl0915.46065
  11. [11] Tabaldyev S.B., On strict homological dimensions of algebras of continuous functions, Math. Notes, 2006, 80(5–6), 715–725 http://dx.doi.org/10.1007/s11006-006-0192-6[Crossref] Zbl1130.46046
  12. [12] Varopoulos N.Th., Some remarks on Q-algebras, Ann. Inst. Fourier (Grenoble), 1972, 22(4), 1–11 http://dx.doi.org/10.5802/aif.432[Crossref] 

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